{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T16:49:15Z","timestamp":1772729355295,"version":"3.50.1"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T00:00:00Z","timestamp":1564358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["274977, 314284"],"award-info":[{"award-number":["274977, 314284"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2019,10,31]]},"abstract":"<jats:p>\n            In this article, we consider the following problem. Given a directed graph\n            <jats:italic>G<\/jats:italic>\n            , output all walks of\n            <jats:italic>G<\/jats:italic>\n            that are sub-walks of all closed edge-covering walks of\n            <jats:italic>G<\/jats:italic>\n            . This problem was first considered by Tomescu and Medvedev (RECOMB 2016), who characterized these walks through the notion of\n            <jats:italic>omnitig<\/jats:italic>\n            . Omnitigs were shown to be relevant for the genome assembly problem from bioinformatics, where a genome sequence must be assembled from a set of reads from a sequencing experiment. Tomescu and Medvedev (RECOMB 2016) also proposed an algorithm for listing all maximal omnitigs, by launching an exhaustive visit from every edge.\n          <\/jats:p>\n          <jats:p>\n            In this article, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>nm<\/jats:italic>\n            )-time algorithm for outputting all the maximal omnitigs of a graph (with\n            <jats:italic>n<\/jats:italic>\n            nodes and\n            <jats:italic>m<\/jats:italic>\n            edges). This is also optimal, as we show families of graphs whose total omnitig length is \u03a9(\n            <jats:italic>nm<\/jats:italic>\n            ). We implement this algorithm and show that it is 9--12 times faster in practice than the one of Tomescu and Medvedev (RECOMB 2016).\n          <\/jats:p>","DOI":"10.1145\/3341731","type":"journal-article","created":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T20:55:51Z","timestamp":1564433751000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["An Optimal\n            <i>O<\/i>\n            (\n            <i>nm<\/i>\n            ) Algorithm for Enumerating All Walks Common to All Closed Edge-covering Walks of a Graph"],"prefix":"10.1145","volume":"15","author":[{"given":"Massimo","family":"Cairo","sequence":"first","affiliation":[{"name":"University of Trento, Povo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Medvedev","sequence":"additional","affiliation":[{"name":"Pennsylvania State University, Pennsylvania, PA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nidia Obscura","family":"Acosta","sequence":"additional","affiliation":[{"name":"Aalto University, Espoo, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2387-0952","authenticated-orcid":false,"given":"Romeo","family":"Rizzi","sequence":"additional","affiliation":[{"name":"University of Verona, Verona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5747-8350","authenticated-orcid":false,"given":"Alexandru I.","family":"Tomescu","sequence":"additional","affiliation":[{"name":"University of Helsinki, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,7,29]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(01)00327-4"},{"key":"e_1_2_1_2_1","volume-title":"28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017","author":"Medvedev Paul","year":"2017"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01194399"},{"key":"e_1_2_1_4_1","first-page":"387","article-title":"Locating well-conserved regions within a pairwise alignment","volume":"9","author":"Chao Kun-Mao","year":"1993","journal-title":"CABIOS"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(94)90049-3"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-010-9334-6"},{"key":"e_1_2_1_7_1","volume-title":"K-best enumeration. Bulletin of the EATCS 115","author":"Eppstein David","year":"2015"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-30850-5_18"},{"key":"e_1_2_1_9_1","first-page":"3","article-title":"A new approach for displaying identities and differences among aligned amino acid sequences","volume":"8","author":"Friemann A.","year":"1992","journal-title":"Comput. Appl. Biosci."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1089\/cmb.1995.2.291"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.11.011"},{"key":"e_1_2_1_12_1","unstructured":"Iu V. L. Florent\u2019ev A. A. Khorlin K. R. Khrapko and V. V. Shik. 1988. Determination of the nucleotide sequence of DNA using hybridization with oligonucleotides. A new method. Doklady Akademii nauk SSSR 303 6 (1988) 1508--1511.  Iu V. L. Florent\u2019ev A. A. Khorlin K. R. Khrapko and V. V. Shik. 1988. Determination of the nucleotide sequence of DNA using hybridization with oligonucleotides. A new method. 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